Kairos
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Gödel's first incompleteness theorem first appeared as "Theorem VI" in Gödel's 1931 paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I". The hypotheses of the theorem were improved shortly thereafter by J. Barkley Rosser (1936) using Rosser's trick. The resulting theorem (incorporating Rosser's improvement) may be paraphrased in English as follows, where "formal system" includes the assumption that the system is effectively generated.
First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F." (Raatikainen 2015)
The unprovable statement GF referred to by the theorem is often referred to as "the Gödel sentence" for the system F. The proof constructs a particular Gödel sentence for the system F, but there are infinitely many statements in the language of the system that share the same properties, such as the conjunction of the Gödel sentence and any logically valid sentence.
Each effectively generated system has its own Gödel sentence. It is possible to define a larger system F’ that contains the whole of F plus GF as an additional axiom. This will not result in a complete system, because Gödel's theorem will also apply to F’, and thus F’ also cannot be complete. In this case, GF is indeed a theorem in F’, because it is an axiom. Because GF states only that it is not provable in F, no contradiction is presented by its provability within F’. However, because the incompleteness theorem applies to F’, there will be a new Gödel statement GF′ for F’, showing that F’ is also incomplete. GF′ will differ from GF in that GF′ will refer to F’, rather than F.
Your universe simulation, theoretically speaking, is a formal system like F. Because you are simulating a universe and that therefore includes rules for things like arithmetic and logic, it is possible to make statements that reach outside of your simulation, referring to the real universe.
This problem happens because a simulation by it's very nature is a formulated system of logical statements and rules. Once you create a system, you open yourself up to this problem. All simulations of sufficient complexity can infer at least some of the computational rules of the real universe from inside the simulation. The real universe just is. It's not a system of rules that excludes other rules. Do you kind of grok what I am telling you? It's alright if you don't. LOTS of people don't get this shit, especially physicists who don't listen to anybody else and refuse to disabuse themselves of the belief that they are the fundamental science.